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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 25094, 24 pages
http://dx.doi.org/10.1155/IJMMS/2006/25094

Fuzzy TL-uniform spaces

Khaled A. Hashem1 and Nehad N. Morsi2

1Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
2Basic & Applied Science Department, Arab Academy for Sciences & Technology and Maritime Transport, P.O. Box 2033, Al-Horraya, Heliopolis, Cairo, Egypt

Received 12 September 2005; Revised 12 April 2006; Accepted 25 April 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main purpose of this paper is to introduce a new structure that is a fuzzy TL-uniform space. We show that our structure generates a fuzzy topological space, precisely, a fuzzy T-locality space. Also, we deduce the concept of level uniformities of a fuzzy TL-uniformity. We connect the category of fuzzy TL-uniform spaces with the category of uniform spaces. We establish a necessary and sufficient condition, under which a fuzzy TL-uniformity is probabilistic pseudometrizable. Finally, we define a functor from the category of fuzzy TL-uniform spaces into the category of fuzzy T-locality spaces and we show that it preserves optimal lifts.